New Developments in Fermionic Many-Body Physics within Time-Dependent Density Functional Theory

Abstract

This thesis documents various recent developments in the physics of systems composedof many strongly interacting fermions, obtained within time-dependent density functional theory, which is a leading microscopic approach for the treatment of the non-equilibrium dynamics of such systems. Various aspects of the problem of nuclear fission are addressed, in particular focusing on the stage of evolution from the outer saddle of the nuclear potential energy surface, through the scission point, and beyond until full separation between the fragments is achieved, for a variety of actinide nuclei. The dynamics of neck rupture during nuclear fission are presented, and it is argued that scission neutrons are expected to be released during this stage. The saddle-to-scission dynamics of nuclei with an odd number of neutrons, and in some cases also an odd number of protons, are presented, which reveal a highly complex nuclear shape evolution and enhanced effects of time-reversal symmetry breaking in such odd systems. The intrinsic spins of the fission fragments are evaluated after scission, and it is found that, with significant probability, the spins are not oriented perpendicular to the fission axis and that their directions in space are correlated. Various aspects of the dynamics of the single-particle occupation numbers, which change in time due to the pairing interaction, are addressed, and these are used to define a notion of complexity for quantum many-body systems. It is also demonstrated that the occupation numbers evolve in time as a non-Markovian stochastic process, both in the case of fission dynamics and also in the case of quantum turbulence and subsequent thermalization of the unitary Fermi gas. Various aspects of the problem of restoring translational invariance of the many- body wave function within density functional theory are presented. Finally, preliminary results are presented concerning the problem of multi-nucleon transfer reactions, treated within time-dependent density functional theory.